Algebra worksheet — GCSE Foundation

1.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

2.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

3.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

4.Solve the inequality 2(3x − 1) ≥ 4x + 8.

5.A number machine multiplies its input by 5. Work out the output when the input is −1.

6.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

7.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

8.Work out the value of 5y + 9 when y = 0

9.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

10.How many turning points does the graph of y = x² − 7x + 10 have?

11.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

12.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

13.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

14.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

15.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.